Factors-11
From Homeworkwiki
Factorize :
(i) a 3 + 27 b 3
(ii) 16 a 4 + 54 a
(iii) 125 a 3 + 1 / 8
(iv) a 3 + b 3 + a + b
Solution :
(i) (i) a 3 + 27 b 3
= ( a ) 3 + ( 3 b ) 3
= (a + 3 b) [ ( a ) 2 - a X 3 b + ( 3 b ) 2 ]
= (a + 3 b) (a 2 - 3 a b + 9 b 2 )
(ii) 16 a 4 + 54 a
= 2 a ( 8 a 3 + 27)
= 2 a [(2 a) 3 + ( 3 ) 3 ]
= 2 a (2 a + 3) (4 a 2 - 6 a + 9)
(iii) 125 a 3 + 1 / 8
= ( 5 a ) 3 + ( 1 / 2 ) 3
= (5 a + 1 / 2) [ ( 5 a ) 2 - 5 a X 1 / 2 + ( 1 / 2 ) 2 ]
= (5 a + 1 / 2) (25 a 2 - 5 a / 2 + 1 / 4 )
(iv) a 3 + b 3 + a + b
= (a + b) (a 2 - a b + b 2 ) + (a + b)
= (a + b) (a 2 - a b + b 2 + 1)
